Machine-learning based control of bi-modular multilevel PWM inverter for high power applications

This paper presents the topology and machine learning-based intelligent control of high-power PV inverter for maximum power extraction and optimal energy utilization. Modular converters with reduced components economic and reliable for high power applications. The proposed integrated intelligent machine learning based control delivers power conversion control with maximum power extraction and supervisory control for optimal load demand control. The topology of the inverter, operating modes, power control and supervisory control aspects are presented. Simulation is carried out in MATLAB/SIMULINK to verify the feasibility of the proposed inverter and control algorithm. The experimental study is presented to validate the simulation results. The operational performance of the proposed topology is evaluated in terms of operational parameters such as regulation of output power, and load relay control and is compared to existing topologies. The economic performance is also evaluated in terms of power switch sizing and reliability in power delivery concerning switch or power sources failure.


Introduction
Large scale photovoltaic (PV) integration to grid and PV assisted electric drives demand for optimal energy consumption for efficient usage of renewable PV sources.The state-of-art converters for PV integration and PV-assisted drives is provided in this section.Also, machine learning algorithms for PV energy estimation and load parameter estimation is reviewed.The recent multilevel inverter topologies [1,2] for PV integration to grid provide single stage conversion, fault tolerance, unbalanced operation.Modularity in these multilevel converters is finding a growing interest owing to power sharing [3,4], distribution of maximum power point (MPP) tracking control [5,6] for independent control and reliability.Topologies with Wave shaping followed by dc-ac stage [6] where sub modules re employed for wave shaping.Parallel connected modules control [7], model predictive control for reduced calculation burden [8], modular converter with flying-capacitor like properties [9], flying-capacitor model with reduced number of components [10], asymmetrical multilevel inverter topologies [11,12], inherent voltage balancing capability modules [13] made modular converters feasible to PV-Grid integration.The merit of modular converters is also validated for variable frequency drives [14,15], power quality enhancement [16], front end rectification [17], energy storage [18].These topologies suffered from increased control complexity, high component count and de-rating of the power switches due to sub-module structures.In parallel, various unconventional topologies were implemented to minimize the component count.Nine different reduced switch topologies were presented in [19] for drives and renewable energy integration.Symmetric and asymmetric staircase cascading multilevel inverter topologies were presented in [16,20].The performance is evaluated in terms of power distribution among modules, blocking voltage, number of switches, switching losses compared to conventional topologies.Switching capacitor topologies also showed good performance for DC-AC conversion [21].However, these unconventional topologies require specially synthesized control structures and are prone to reliability considerations.The Reliability study [22,23] and efficient component sizing [24] are key commercial power conversion aspects.In this context, high-power PV integration needs multilevel inverters with modularity and fewer components for reliable operation and semi-conductor footprint reduction [25,26].Utilization of heuristic and artificial intelligent techniques for power control in renewable energy systems integrated to grid was reported [27,28] in which atom search optimization, fuzzy logic-based control, predictive control was adopted for efficient and robust control.
Various machine learning applications are developed which include policy approximations for energy management in PV systems [29], energy loss assessment foe PV sizing and ensemble learning for fault detection in PV systems [30], machine learning for PV energy forecasting [3], clustering and deep learning algorithms for energy estimation [31], Adaline neural networks [32], energy management systems [33] for improved forecasting methods for capacity firming.All these technologies and methodologies involve multiple-stage conversion, complex algorithms, and convergence.
Therefore, the present work attempts to combine the reliability merit of modularity with the reduced component count.A bi-modular multilevel inverter is developed which could provide any level voltage between seven and nineteen with the semi-conductor switch component count equal to that of conventional five level inverters.Also, machine learning-based supervisory control for PV power estimation and corresponding load demand control is presented.
The rest of the paper is organized as follows.Section 2 presents the switching logic and control of the inverter.Section 3 presents control algorithm.Section 4 presents simulation study of the proposed topology.Section 5 presents the experimental validation of inverter performance.Section 6 presents conclusions.

Bi-modular multilevel inverter
The schematic of the modular multilevel inverter is illustrated in Fig 1 .DC voltages are in the ratio 1:2:6, respectively [34] as shown in Fig 1 .Each module has two functions viz.voltage level generation and polarity generation.The H-Bridge in the modules generate polarity.Asymmetrical switches in module 2 (Sb3, Sb4, Sb5, Sb6) generate three different voltage levels.The cascaded modules therefore generate a respective voltage level as the algebraic sum of voltage of the two modules.

Switching combinations for output voltage levels generation
The switching combinations to achieve each level in positive half cycle of output voltage is shown in Fig 2 .The switches turned ON in respective module were identified along with the flow of current in each switch and load.Each module's contribution to generating respective to Module 2 H-bridge respectively with corresponding asymmetric switches turned ON generate +7/9 V DC and + 8/9 V DC .

Pulse width modulation and output voltage
The output frequency sinusoidal reference signal is compared to level shifted modified triangular carrier signals as shown in Fig 6 .An asymmetrical carrier width is produced to improve the switching behavior, increasing the apparent switching frequency.The expression for unit template of carrier waveform pertaining to k th switching period is given as Where, T is period for one switching cycle with o s ¼ 2p T is the angular switching frequency.Then, the level shifted carrier waveforms are given as for x = 0, 1, 2, . ....18 represent the eighteen level shifted carrier waveforms.
The reference sinusoidal signal is given as With |M|�1 and ω r is the reference angular frequency for the output voltage waveform.
The following implicit relations represent the switching instants in each switching period for different carrier waveforms with natural sampling.
Where, A a ðxÀ 9Þk , and B a ðxÀ 9Þk are leading and trailing switching instants of x th carrier in k th switching period.
The pulse width modulated (PWM) signal generates two states viz. 1 and 0 respectively for reference wave above and below carrier wave which is given as follows Then, the output voltage is the algebraic sum of pulse width modulated waveforms develop by each carrier raised by a factor of MV DC .Thus, the output voltage whose Fourier series representation is given as The PWM first stage PWM patterns obtained from Eq (6) are designated as 1 to 9 and -1 o -9 in Table 1.Now, from the operational modes explained from Fig 2 the contribution of each switch to different output voltage levels is obtained.Thus, the gating signals for each switch are obtained by logical OR operations of all such PWM patterns for which the respective switch contribution is required.

Machine learning based control of converter
Machine learning based control is utilized for power flow control and optimal load scheduling.The control objectives include extracting maximum power corresponding to irradiance at any given instance, delivery of power to load at regulated voltage, and estimation of PV power for succeeding time intervals for time shifting of allowable loads for optimization of PV energy consumption.

Reinforcement learning ANN training for MPP and PV power estimation
Multi-layer reinforcement learning artificial neural network (ANN) is employed for pattern recognition type machine learning to estimate MPP and hourly PV power due to its ability to

Power control and load scheduling
Voltages and currents of PV arrays are sensed to determine voltage corresponding to maximum power.Control for extracting MPP is shown in Fig 12 .The voltage and current are utilized to determine PV array power.The difference in PV power samples along with gradient of PV power fed as input to ANN determines the direction and step size in each iteration to track the maximum power point.Control of single stage modular inverter is also shown in Fig 12.
The error in obtained DC voltage from MPP control and actual PV array voltage serve as input to PI controller which determine the modulation ratio of the reference sinusoidal current waveform for regulation of motor phase voltage to set value.The phase reference is obtained from zero crossing instants of respective set phase voltages.The product of these two   aggregated in every sample.These two inputs are provided to multi-layer ANN with the training pattern similar to that of MPP estimation determines the hourly estimation of PV power.
A look-up table then determines the load relay status based on the pre-set load priority.

Simulation results
The Simulation of inverter with proposed integrated intelligent control is carried out in MATLAB/SIMULINK.The simulation parameters are given in Table 3.The performance is evaluted in terms of efficient power conversion and load schedule.Simulation results for these aspects are presented in this section.

Power flow control
The simulated output voltage regulation of the inverter is shown in Figs

Load relay control
The simulated output for load relay control is shown in  priority load is always scheduled to be turned ON with minimum power availability of 0.3 pu.Load 2 with the next higher priority is scheduled to turned ON for PV power estimation greater than 0.5 pu.Load 3 with least priority is s scheduled to turned ON for PV power estimation greater than 0.75 pu.

Experimental validation and performance evaluation
A hardware setup is developed to modular inverter.The parameters and hardware modules utilized are provided in Table 4.The experimental setup is shown in Fig 20 .The proposed control is realized through Artix 7 FPGA controller.

Power flow control
The modulated gating pulses pertaining to instance of irradiance is depicted in

Load scheduling
The estimated PV power from power aggregator and power gradient control the load relays which are scheduled to turned ON for PV power estimation greater than 0.5 pu for Load 2 and greater than 0.75 pu for Load 3 which is seen from Fig 27.

Converter sizing and reliability evaluation
The rms voltage and current ratings are measured and per unit voltage and current sizing is provided in Table 5.
Another figure of merit for the proposed control is that utilizing modular nature of the converter the modulation index obtained from supervisory control determines the output levels of A comparison is made in terms of minimum output power delivered by the inverter under module or source failure is presented in Table 6.The proposed inverter with its topological structure proved minimum of 56 percent power availability for any component failure in comparison to existing similar switch count asymmetrical multilevel inverters.
A comparison among the existing and proposed modular inverters is made in terms of number of levels in output voltage, and sizing of power switches.The proposed bi-modular achieved more than 50 percent reduction in voltage and current sizing compared to conventional H-bridge [26] inverters with similar switch count.Also, Table 7 depicts the comparison of sizing with asymmetrical inverters in which the proposed converter proved reduced size with existing asymmetrical inverters.

Conclusions
A bi-modular nineteen-level PWM voltage source inverter is developed for high-power applications.The proposed inverter is controlled with machine learning-based control for extracting MPP, inverter power control and PV power estimation.The MPP extraction is achieved with 99.9 percent accuracy.The machine learning algorithms accurately determine the modulation of inverter voltage for changing MPP.The presented twelve-switch modular inverter validated a nineteen-level output voltage 2.7 times higher than conventional similar switch count topologies.The performance of the proposed inverter is proved compatible over reasonable power factor range and modulation range.Also, a reduction by 20 percent is obtained in terms of power switch sizing compared to similar power handling conventional topologies.The reliability study proved its redundancy by 56 percent.Thus, this inverter topology and  control algorithm can be implemented for high power applications for efficient and reliable power electronic interfaces.

Fig 6 .
Fig 6.Reference signal and level shifted modified triangular carrier for the first stage PWM signals generation.https://doi.org/10.1371/journal.pone.0305759.g006 recognize various patterns and cluster them for provided input-output combination.This is highly suitable for varied conditions of irradiance under different days of different seasons to produce large variety of power variance combinations.The scheme of machine learning is shown in Fig 7 which consists of ΔP PV (i.e.P PV (k)-P PV (k-1)) as input with multiple reinforcement training middle layers and the acceleration factor α as the output.The detailed training algorithm in shown in Fig 8 in which the input data samples are clustered in to subsets in various epoch which undergo several iterations until the error in power estimation reaches threshold value.The training sets as shown in Table 2 is utilized for machine learning.The completed data utilized for training is provided in S1-S4 Files.The training of multi-layer ANN for MPP tracking and load demand control is depicted in Figs 9 and 10.The convergence was obtained at eighth epoch of training.The regression for training, validation and training data sets was observed in Fig 9 which depicts accuracy to of the training to target output data.The gradient of mean of squared error and validation checks were shown in Fig 10 which also depict the convergence of the neural network.The validation of estimation is shown in Fig 11 in which larger set of instances proved closeness to zero error.

Fig 19 .
The estimated PV power from power aggregator and power gradient obtained is shown in Fig 19.Load 1 being the high